An approach to spherical kinematics using tools suggested by plane kinematics

There are striking analogies between plane kinematics and spherical kinematics. For instance the theorems of Kennedy, Euler-Savary, Bobillier from plane kinematics have their counterparts in spherical kinematics. It is well-known that a treatment of the elementary part of plane kinematics can be based upon the right-angle theorem: i.e. if a right angle moves in such a way that the vertex follows a fixed curve while one of its sides remains tangential to this curve at the vertex, the pole of the motion coincides with the centre of curvature of the fixed curve corresponding with the vertex. In this paper it is shown that this theorem can be carried over in a simple way to spherical kinematics and that the elementary part of spherical kinematics can be founded on it.